函数f(x)=x(x-1)(x-2)(x-3)...(x-100)在x=0处的导数值为?紧急!如题!紧急!
问题描述:
函数f(x)=x(x-1)(x-2)(x-3)...(x-100)在x=0处的导数值为?紧急!
如题!紧急!
答
100!
答
f(x)=x(x-1)(x-2)(x-3)...(x-100)
f'(x)=(x-1)(x-2)(x-3)...(x-100)+x*[(x-1)(x-2)(x-3)...(x-100)]'
所以:
f'(0)=1*2*3.....*100+0
=100!
答
是0啊,把前两项看成一项,后面看成一项,则先对x(x-1)求导得2x,后面的就不用问了,因为x=0.